# Trapezoid, Midpoint and Simpson integrations

## Calculate a table of the integrals of the given function f(x) over the interval (a,b) using Trapezoid, Midpoint and Simpson's methods.

 The integrand f(x) is assumed to be analytic and non-periodic.It is calculated by increasing the number of partitions to double from 2 to N.
f(x)
a
 , b
 maximum partition N 32 64 128 256 512 1024 2048
 6dgt10dgt14dgt18dgt22dgt26dgt30dgt34dgt38dgt42dgt46dgt50dgt

 $\normal \hspace{40}S={\large\int_a^{\hspace{25}b}}f(x)dx\\(1)\ Trapezoid\hspace{5}S_{\normal t}={\large\frac{b-a}{2}}\{f(a)+f(b)\}\\(2)\ Midpoint\hspace{10}S_m=(b-a)f({\large\frac{a+b}{2}})\\(3)\ Simpson\hspace{10}S_{\normal s}={\large\frac{S_{\normal t}+2S_m}{3}}\\\hspace{105}={\large\frac{b-a}{6}}\[f(a)+4f({\large\frac{a+b}{2}})+f(b)\]\\$

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